Gyroscopes or gyro rate sensors are widely used for navigation, stabilization, general rate control, pointing, autopilot systems, missile guidance control, etc. A typical example is the application of yaw rate sensors to automobiles to provide input to the control systems for suspension, braking and steering. During recent years there have been attempts to develop low cost gyroscopes suitable for mass production. A promising concept of such a device is the vibratory gyroscope which can be fabricated using surface-micromachining technology.
The basis operating principle of a vibratory gyroscope 10 is illustrated in FIG. 1. The purpose of the gyroscope 10 is to measure the angular velocity .OMEGA.. To achieve this, it is first necessary to cause the particle 12 to vibrate with constant amplitude along the axis Ox. This motion is referred to as primary motion (or driven motion). When the gyroscope 10 rotates, the particle 12 experience a Coriolis inertia force. This force has a magnitude proportional to .OMEGA. and a direction along the axis Oy. In the absence of further control on the motion of the particle 12, the Coriolis force will cause the particle 12 to vibrate along the axis Oy. This motion is referred to as secondary motion (or sensing motion) and a measurement of its amplitude will provide an estimate of the angular velocity .OMEGA..
The sensitivity of such a vibratory gyroscope can be determined by: ##EQU1##
Where:
Yo is the magnitude of the sensing motion; PA1 .OMEGA. is the angular rate applied to the gyroscope; PA1 .omega..sub.x is the excitation frequency of the driven motion in the axis Ox; PA1 .omega..sub.y is the resonant frequency of the sensing motion in the axis Oy; PA1 r=.omega..sub.x /.omega..sub.y ; and PA1 Q is the mechanical quality factor for the sensing motion.
It can be seen from the foregoing equation that, when r=.omega..sub.x /.omega..sub.y =1, the sensitivity can reach its maximum value, i.e., ##EQU2##
Assuming that X.sub.o =1 .mu.m, .omega..sub.y =K.sub.y +L /m=6879 Hz and the gyro is vacuum packaged so that Q.apprxeq.10000. One can get the sensitivity, ##EQU3##
For the input of unit angular rate, .OMEGA.=1 .sup.0 /s=0.0174 rad/s the amplitude of the sensing motion is: EQU Y.sub.o =8.07.times.10.sup.-9 m=8.07 nm
It can be thus understood that the sensing motion is the secondary effect of the Coriolis force. Note that the above estimate is based on various idealizations and assumptions. In practice, the real magnitude of the sensing motion could be far below this value, e.g., a few angstroms. Such a tiny magnitude of the sensing motion presents a major difficulty in measurement, especially if the motion is detected capacitively. It is therefore necessary to seek a proper structural design so that the sensitivity of the vibratory gyroscope can be improved.